2.1056   ODE No. 1056

\[ x^2 \left (-y'(x)\right )+y''(x)+x y(x)=0 \]

✓ Mathematica : cpu = 0.0676594 (sec), leaf count = 41

DSolve[x*y[x] - x^2*Derivative[1][y][x] + Derivative[2][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to c_1 x-\frac {c_2 \sqrt [3]{-x^3} \Gamma \left (-\frac {1}{3},-\frac {x^3}{3}\right )}{3 \sqrt [3]{3}}\right \}\right \}\]

✓ Maple : cpu = 0.133 (sec), leaf count = 51

dsolve(diff(diff(y(x),x),x)-x^2*diff(y(x),x)+x*y(x)=0,y(x))
 

\[y \left (x \right ) = x c_{1} +c_{2} \left (3^{{2}/{3}} \left (-x^{3}\right )^{{1}/{3}} \Gamma \left (\frac {2}{3}\right )-3^{{2}/{3}} \left (-x^{3}\right )^{{1}/{3}} \Gamma \left (\frac {2}{3}, -\frac {x^{3}}{3}\right )+3 \,{\mathrm e}^{\frac {x^{3}}{3}}\right )\]